
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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43

Transcribed Image Text:2z = 4
n degrees
ds is
mea-
S
ture
erage
mate
C/year
also
2
ction,
salinity
16D
is the
ow the
y dive
ng
O of
by the
(min)
ing as
how the current I is changing at the moment when R 400 2,
= -0.01 V/s, and dR/dt = 0.03 /s.
IR, to find
1 = 0.08 A, dv/dt
41. The pressure of 1 mole of an ideal gas is increasing at a rate
of 0.05 kPa/s and the temperature is increasing at a rate of
0.15 K/s. Use the equation PV = 8.31T in Example 2 to find
the rate of change of the volume when the pressure is 20 kPa
and the temperature is 320 K.
42. A manufacturer has modeled its yearly production function P
(the value of its entire production, in millions of dollars) as a
Cobb-Douglas function
P(L, K) = 1.47L0.65 K0.35
where L is the number of labor hours (in thousands) and K is
the invested capital (in millions of dollars). Suppose that when
L= 30 and K = 8, the labor force is decreasing at a rate of
2000 labor hours per year and capital is increasing at a rate of
$500,000 per year. Find the rate of change of production.
43. One side of a triangle is increasing at a rate of 3 cm/s and a
second side is decreasing at a rate of 2 cm/s. If the area of the
triangle remains constant, at what rate does the angle between
the sides change when the first side is 20 cm long, the second
side is 30 cm, and the angle is π/6?
48. If z =
44. A sound with frequency f, is produced by a source traveling
along a line with speed vs. If an observer is traveling with
speed v, along the same line from the opposite direction toward
the source, then the frequency of the sound heard by the
observer is
fo=
=
49-54 Assum
second-order
49. Show tha
-[f
is a solu
[Hint:
50. If u =
c + vo
C - Vs
where c is the speed of sound, about 332 m/s. (This is the
Doppler effect.) Suppose that, at a particular moment, you
are in a train traveling at 34 m/s and accelerating at 1.2 m/s².
A train is approaching you from the opposite direction on the
other track at 40 m/s, accelerating at 1.4 m/s², and sounds its
whistle, which has a frequency of 460 Hz. At that instant, what
is the perceived frequency that you hear and how fast is it
changing?
51. If z
(Con
52. If z
(a)
53. If a
54. S
C
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